CN117828419B - Mine gas concentration prediction method based on optimization variation modal decomposition - Google Patents
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Abstract
The invention discloses a mine gas concentration prediction method based on optimization variation modal decomposition, which comprises the steps of decomposing data into a plurality of intrinsic modal components IMFs with different center frequencies through improved variation modal decomposition IVMD, solving the decomposition modal number of VMDs to realize the self-adaptive selection of the modal number, dividing each IMF into a training set and a testing set, respectively establishing a KELM prediction model based on JAYA optimization for preliminary prediction, performing prediction error prediction on the prediction error of each IMF by adopting a cyclic error compensation CEC, and finally superposing the prediction results of all the IMFs and the prediction results of the prediction errors of the IMFs to obtain a final prediction result. The invention can realize higher accuracy on the premise of multi-step prediction work, especially at some extreme points, can provide important information for coal mine gas safety early warning, and can provide important theoretical basis and data support for coal mine gas safety early warning.
Description
Technical Field
The invention relates to a mine gas concentration prediction method, in particular to a mine gas concentration prediction method based on optimization variation modal decomposition, and belongs to the technical field of coal mine safety production.
Background
The mine dynamic disaster is caused by mine excavation, takes a mine body or rock mass, water, gas mixture and the like as a carrier, accidentally releases energy in a dynamic mode, and acts on a roadway, a working face, engineering structures or human bodies, and comprises mine earthquake, rock burst, coal and gas outburst, abnormal gas emission, roof caving, water burst, water permeation and the like. For coal mines, gas dynamic disasters are the most important threat of coal mine safety production, and as the coal mining depth increases, the gas dynamic disasters often produce more complex mine dynamic disasters through the joint coupling action of the gas dynamic disasters and rock burst dynamic disasters, so that the rapid and accurate gas prediction has important significance for effective gas control.
The existing gas concentration data prediction methods mainly comprise three methods, namely: prediction methods based on traditional statistical theory, prediction methods based on machine learning and prediction methods based on modal decomposition. The prediction method based on the traditional statistical theory mainly comprises an autoregressive method, an autoregressive moving average method, an autoregressive comprehensive moving average method and the like, and the models perform well in linear stable time sequence prediction, but the prediction accuracy of the models in mine gas concentration data is not ideal because the mine gas concentration data has the characteristics of strong randomness and non-stationarity. Prediction methods based on machine learning have proven to have good effects in processing mine gas concentration data with strong randomness and non-stationarity, but the methods often need to manually set some super parameters, have general precision and stability, still have a small error rate, and are less developed in multi-step prediction work. The method based on modal decomposition is a method based on data driving, the method is used for analyzing mine gas data, characteristics in the data are mined, and high prediction accuracy can be achieved, but most of the existing prediction methods based on modal decomposition are based on empirical mode decomposition, the problem of modal aliasing exists, the prediction accuracy is greatly affected, in addition, the existing prediction methods based on variable modal decomposition are sensitive to parameter setting, the number of modes cannot be solved in a self-adaptive mode, when the number of modes is selected improperly and when signals contain high noise levels, accuracy and stability of decomposition results are affected, and the prediction effect is poor.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides the mine gas concentration prediction method based on optimization variation modal decomposition, which can realize higher accuracy on the premise of multi-step prediction work, and further can provide important theoretical basis and data support for coal mine gas safety early warning.
In order to achieve the purpose, the mine gas concentration prediction method based on optimization variation modal decomposition is IVMD-JKELM-CEC and specifically comprises the following steps:
Step1, collecting mine gas concentration data, selecting N data as experimental data, preprocessing the experimental data, performing interpolation filling processing on abnormal values and missing values by adopting smooth interpolation, and performing normalization processing on the experimental data;
Step2, decomposing the normalized experimental data into a plurality of intrinsic mode components IMFs with different center frequencies through improved variation mode decomposition IVMD, and solving the decomposition mode number of the VMD by using a center frequency minimum difference quotient algorithm to realize the self-adaptive selection of the mode number;
Step3, dividing each IMF obtained by IVMD decomposition into a training set and a testing set, respectively establishing a KELM prediction model based on JAYA optimization for each IMF, completing preliminary prediction of the IMF, and obtaining a prediction result
Step4, predicting the prediction error of each IMF by adopting a cyclic error compensation CEC to complete the prediction of the prediction error of the IMF, and obtaining a prediction result Y E＝{E1,E2,...,Ei;
step5, superposing all the prediction results of the IMFs and the prediction results of the IMF prediction errors as follows
Y＝Y*+YE
And obtaining a final prediction result Y.
Further, in Step2, the normalized experimental data is decomposed into a plurality of natural modal components IMF with different center frequencies by the improved variational modal decomposition IVMD as follows:
The analytic signal of each modal function is obtained through Hilbert transformation, the analytic signal is multiplied by the estimated center frequency e -jωkt, the analytic signal is modulated to the corresponding base frequency spectrum, the square of the two norms of the gradient of the analytic signal is estimated through Gaussian smoothing, the signal bandwidth of each modal component is obtained, and a constrained variation model is obtained as follows:
wherein: u k is the modal component of the beam, Representing the bias derivative, delta (t) representing the dirac distribution, { omega k } being the set of center frequencies, K being the modal number, f being the original signal;
penalty factors alpha and Lagrange multipliers lambda (t) are introduced, and the solution is carried out by adopting an alternating direction operator method, so that each modal component and the center frequency are obtained as follows:
Wherein: Is a modal component,/> Is the center frequency.
Further, in Step2, the algorithm of the minimum difference quotient of the center frequency is specifically as follows:
initializing the minimum value and the maximum value of the decomposition modal value, wherein the minimum value is 2, and the maximum value is not more than 15;
Decomposing mine gas concentration data y into M IMFs by utilizing VMD, and calculating center frequency difference delta omega of adjacent IMFs, wherein the mean value of delta omega is expressed as:
the center frequency minimum difference quotient DQ is expressed as follows:
M stops iterating when the termination condition of the following formula is reached:
The exact number of modes k=m-3 at this time.
Further, in Step3, the training set and the testing set are specifically as follows for each IMF divided by IVMD:
For mine gas concentration data x= [ X 1,x2,x3...,xn ], wherein X i is mine gas concentration data at the i-th time; and predicting X by using a sliding prediction mode, wherein the window size is m, wherein m is more than or equal to 2, and dividing X into n-m windows, wherein the 1 st window W 1＝[x1,x2,...,xm-1,xm, the i th window W i＝[xi,xi+1,...,xi+m-2,xi+m-1, the last window W n-m＝[xn-m,xn-m+1,...,xn-2,xn-1 and the output of the multi-step prediction are multiple.
Further, when a KELM prediction model based on JAYA optimization is respectively built for each IMF, a kernel function is introduced, the kernel function matrix is Ω KELM＝HHT, the element is Ω KELM(i,j)＝h(xi)h(xj)＝K(xi,xj), and then the output of KELM is:
Wherein: i is a diagonal matrix, C is a regularization coefficient, and T is a desired output matrix;
KELM is a RBF kernel function, and the formula is:
Where λ is the kernel parameter.
Further, using JAYA to perform optimization calculation on the kernel parameters and regularization coefficients of KELM, wherein the fitness evaluation function is as follows:
wherein: y (i) is a prediction result, and y d (i) is a desired output.
Further, step4 specifically includes the following steps:
Step4-1, dividing the data according to windows, and predicting the data by JKELM to obtain n-m predicted gas concentration data;
Step4-2, performing difference between the predicted gas concentration data and the actual value to obtain layer 1 error data E 1, continuously predicting E 1 to obtain m-2n predicted error data, namely layer 2 error data E 2, and so on, and obtaining m-in predicted error data, namely layer i error data E i in the ith layer;
step4-3, setting the termination condition of error calculation as follows: 5|E A i-Ei-1|＜Ei-1
Compared with the prior art, the mine gas concentration prediction method based on optimization variation modal decomposition comprises the steps of decomposing data into a plurality of inherent modal components IMFs with different center frequencies through improved variation modal decomposition IVMD, solving the decomposition modal number of the VMD through a center frequency minimum difference quotient algorithm to achieve adaptive selection of the modal number, dividing each IMF obtained through IVMD decomposition into a training set and a test set, respectively establishing a KELM prediction model based on JAYA optimization for each IMF, completing preliminary prediction of the IMFs, predicting prediction errors of each IMF through cyclic error compensation CEC, completing prediction of the prediction errors of the IMFs, and finally superposing the prediction results of all the IMFs and the prediction results of the prediction errors of the IMFs to obtain a final prediction result.
Drawings
FIG. 1 is a flow chart of a mine gas concentration prediction method based on IVMD-JKELM-CEC of the present invention;
FIG. 2 is a flowchart of the algorithm of the invention IVMD;
FIG. 3 is a graph showing the decomposition results of mine gas concentration data IVMD after treatment according to the present invention;
FIG. 4 is a schematic diagram of a cyclic error compensation execution flow of the present invention;
FIG. 5 is a time domain diagram of single step prediction results of mine gas concentration data according to an embodiment of the present invention;
FIG. 6 is a time domain diagram of 10-step prediction results of mine gas concentration data according to an embodiment of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
As shown in FIG. 1, the mine gas concentration prediction method based on optimization variation modal decomposition is IVMD-JKELM-CEC, and specifically comprises the following steps:
step1, collecting mine gas concentration data, and selecting N data as experimental data. And preprocessing experimental data, adopting smooth interpolation to perform interpolation filling processing on abnormal values and missing values, and further performing normalization processing on the experimental data.
Step2, as shown in fig. 2, decomposes the normalized experimental data into a plurality of intrinsic mode components IMFs with different center frequencies through improved variation mode decomposition IVMD, and solves the decomposition mode number of the VMD through a center frequency minimum difference quotient algorithm, thereby realizing the self-adaptive selection of the mode number. Specific:
Step2-1, construction variation problem: obtaining an analytic signal of each mode function through Hilbert transformation, and multiplying the analytic signal by an estimated center frequency Modulating the signal into a corresponding basic frequency spectrum, and obtaining the signal bandwidth of each modal component by estimating the square of the binary norm of the gradient of the analytic signal through Gaussian smoothing, thereby obtaining a constrained variation model:
wherein: u k is the modal component of the beam, Represents the bias derivative, delta (t) represents the dirac distribution, { omega k } is the set of center frequencies, K is the modal number, and f is the original signal.
Step2-2, solving a variational problem: and introducing a penalty factor alpha and a Lagrangian multiplier lambda (t) to convert the constraint variation problem into an unconstrained variation problem. Solving by adopting an alternating direction operator method to obtain each modal component and the center frequency as follows:
Wherein: Is a modal component,/> Is the center frequency.
Step2-3, initializing the minimum value and the maximum value of the decomposition modal value, wherein the minimum value is 2, and the maximum value is not more than 15.
Step2-4, decomposing mine gas concentration data y into M IMFs by using VMD, and calculating center frequency difference delta omega of adjacent IMFs, wherein the mean value of delta omega is expressed as:
step2-5, the center frequency minimum difference quotient DQ may be expressed as follows:
Step2-6, the DQ value will gradually decrease as the number of signal decomposition modes increases. After exceeding the correct number of modes, the DQ values will settle. M stops iterating when the termination condition of the following formula is reached:
At this time, the accurate mode number is k=m-3, and the result of decomposing mine gas concentration data IVMD is shown in fig. 3.
Step3, dividing each IMF obtained by IVMD decomposition into a training set and a testing set, respectively establishing a KELM prediction model (namely JKELM prediction model) based on JAYA optimization for each IMF, and completing preliminary prediction of the IMF to obtain a prediction resultSpecific:
Step3-1, dividing a training set and a testing set for each IMF obtained by IVMD decomposition, and obtaining mine gas concentration data X= [ X 1,x2,x3...,xn ], wherein X i is mine gas concentration data at the ith moment; and predicting X by using a sliding prediction mode, wherein the window size is m, wherein m is more than or equal to 2, dividing X into n-m windows, a1 st window W 1＝[x1,x2,...,xm-1,xm, an ith window W i＝[xi,xi+1,...,xi+m-2,xi+m-1 and a last window W n-m＝[xn-m,xn-m+1,...,xn-2,xn-1. The multi-step prediction only needs to be output in a plurality.
Step3-2, a KELM predictive model is built for each IMF. KELM as an improved version of ELM, to which a kernel function is introduced. The kernel function matrix is Ω KELM＝HHT, its element is Ω KELM(i,j)＝h(xi)h(xj)＝K(xi,xj), then the output of KELM is:
wherein: i is a diagonal matrix, C is a regularization coefficient, and T is a desired output matrix.
KELM is a RBF kernel function, and the formula is:
Where λ is the kernel parameter.
Step3-3, using JAYA to perform optimization calculation on the kernel parameters and regularization coefficients of KELM, wherein the fitness evaluation function is as follows:
wherein: y (i) is a prediction result, and y d (i) is a desired output.
Step4, as shown in fig. 4, predicting the prediction error of each IMF by adopting cyclic error compensation CEC, so as to complete the prediction of the prediction error of the IMF, and obtain a prediction result Y E＝{E1,E2,...,Ei }. The cyclic error compensation CEC is adopted to predict the prediction error, so that the single-step prediction error and the multi-step prediction error can be compensated, the prediction precision is further improved, and the method specifically comprises the following steps:
Step4-1, dividing the data according to windows, and predicting the data by JKELM to obtain n-m predicted gas concentration data.
Step4-2, performing difference between the obtained predicted gas concentration data and the actual value to obtain layer 1 error data E 1, continuously predicting E 1 to obtain m-2n predicted error data, namely layer 2 error data E 2, and obtaining m-in predicted error data, namely layer i error data E i in the ith layer.
Step4-3, the prediction accuracy can be improved through CEC, but when the iteration times are too many, the prediction result is scattered, so that the prediction result accuracy is reduced. The termination conditions for error calculation are thus set as:
5|Ei-Ei-1|＜Ei-1
Step5, superposing all the prediction results of the IMFs and the prediction results of the prediction errors of the IMFs to complete the prediction, namely Y=Y *+YE.
In order to verify the effectiveness of the mine gas concentration prediction method based on optimization variation modal decomposition, the following accuracy evaluation indexes are adopted: mean absolute error (Mean Absolute Error, MAE), standard root mean square error (Root Mean Square Error, RMSE), determinable coefficient (Coefficient of determination, R 2). The smaller the values of RMSE and MAE, the higher the prediction accuracy, and the larger the value of R 2, the higher the prediction accuracy. The calculation formulas are respectively as follows:
Wherein: Is the predicted value of the model, y t is the true value,/> Average value of source data.
5000 Data of a coal mine gas working face in Shanxi of China are selected, the time resolution is 2 minutes, the first 80% is used as a training set, and the second 20% is used as a test set. The result of the decomposition of the processed mine gas concentration data through IVMD is shown in fig. 3. And then training and predicting the decomposed data by JKELM, and performing error compensation by adopting cyclic error compensation to obtain a final prediction result. The common time sequence prediction model BP neural network, ELM neural network and KELM neural network are selected as comparison, and five models of EMD-JKELM, EMD-JKELM-CEC, CEEMDAN-JKELM, CEEMDAN-JKELM-CEC and VMD-JKELM are selected as comparison. The single-step prediction accuracy evaluation index values are shown in table 1 below, and the 10-step prediction experiment result accuracy evaluation index values are shown in table 2 below.
Table 1 single step prediction experiment result accuracy evaluation index value
TABLE 2 evaluation index value for accuracy of 10-step predictive test result
As can be seen from Table 1, the mine gas concentration prediction method (IVMD-JKELM-CEC) based on optimization variation modal decomposition has the highest prediction junction precision, and the prediction results of the EMD-JKELM, CEEMDAN-JKELM and IVMD-JKELM are improved by a certain program after error correction. As shown in FIG. 5, the predicted result and the true value of BP, ELM, KELM have poor fitting degree, and the fitting degree is improved to different degrees after the modal decomposition treatment, wherein the fitting degree of the mine gas concentration prediction method (IVMD-JKELM-CEC) based on the optimized variation modal decomposition is the highest. As can be seen from Table 2, the 10-step prediction was overall worse than the single-step prediction, and the prediction accuracy of the present mine gas concentration prediction method (IVMD-JKELM-CEC) based on the optimal variation modal decomposition was highest among all the results. As shown in FIG. 6, the fitting degree of the predicted result of the 10-step prediction is worse than that of the single-step prediction, but the detail graph shows that the fitting degree of the mine gas concentration prediction method (IVMD-JKELM-CEC) based on the optimization variation modal decomposition is superior to other models, especially at some extreme points, important information can be provided for coal mine gas safety early warning, and important theoretical basis and data support can be provided for coal mine gas safety early warning.
Claims (7)
1. The mine gas concentration prediction method based on optimization variation modal decomposition is characterized by comprising the following steps of:
Step1, collecting mine gas concentration data, selecting N data as experimental data, preprocessing the experimental data, performing interpolation filling processing on abnormal values and missing values by adopting smooth interpolation, and performing normalization processing on the experimental data;
Step2, decomposing the normalized experimental data into a plurality of intrinsic mode components IMFs with different center frequencies through improved variation mode decomposition IVMD, and solving the decomposition mode number of the VMD by using a center frequency minimum difference quotient algorithm to realize the self-adaptive selection of the mode number;
Step3, dividing each IMF obtained by IVMD decomposition into a training set and a testing set, respectively establishing a KELM prediction model based on JAYA optimization for each IMF, completing preliminary prediction of the IMF, and obtaining a prediction result
Step4, predicting the prediction error of each IMF by adopting a cyclic error compensation CEC to complete the prediction of the prediction error of the IMF, and obtaining a prediction result Y E＝{E1,E2,...,Ei;
step5, superposing all the prediction results of the IMFs and the prediction results of the IMF prediction errors as follows
Y＝Y*+YE
And obtaining a final prediction result Y.
2. The mine gas concentration prediction method based on optimized variation modal decomposition according to claim 1, wherein in Step2, the normalized experimental data is decomposed into a plurality of natural modal components IMF with different center frequencies by the improved variation modal decomposition IVMD as follows:
Obtaining an analytic signal of each modal function by Hilbert transformation, multiplying the analytic signal by an estimated center frequency Modulating the signal into a corresponding basic frequency spectrum, and estimating the square of the binary norm of the gradient of the analytic signal through Gaussian smoothing to obtain the signal bandwidth of each modal component, wherein the constrained variation model is obtained as follows:
wherein: u k is the modal component of the beam, Representing the bias derivative, delta (t) representing the dirac distribution, { omega k } being the set of center frequencies, K being the modal number, f being the original signal;
penalty factors alpha and Lagrange multipliers lambda (t) are introduced, and the solution is carried out by adopting an alternating direction operator method, so that each modal component and the center frequency are obtained as follows:
Wherein: Is a modal component,/> Is the center frequency.
3. The mine gas concentration prediction method based on optimized variation modal decomposition according to claim 2, wherein in Step2, the minimum difference quotient algorithm of the center frequency is specifically as follows:
initializing the minimum value and the maximum value of the decomposition modal value, wherein the minimum value is 2, and the maximum value is not more than 15;
Decomposing mine gas concentration data y into M IMFs by utilizing VMD, and calculating center frequency difference delta omega of adjacent IMFs, wherein the mean value of delta omega is expressed as:
the center frequency minimum difference quotient DQ is expressed as follows:
M stops iterating when the termination condition of the following formula is reached:
The exact number of modes k=m-3 at this time.
4. The mine gas concentration prediction method based on optimized variation modal decomposition according to claim 1, wherein in Step3, each IMF obtained by the IVMD decomposition is divided into a training set and a testing set as follows:
For mine gas concentration data x= [ X 1,x2,x3...,xn ], wherein X i is mine gas concentration data at the i-th time; and predicting X by using a sliding prediction mode, wherein the window size is m, wherein m is more than or equal to 2, and dividing X into n-m windows, wherein the 1 st window W 1＝[x1,x2,...,xm-1,xm, the i th window W i＝[xi,xi+1,...,xi+m-2,xi+m-1, the last window W n-m＝[xn-m,xn-m+1,...,xn-2,xn-1 and the output of the multi-step prediction are multiple.
5. The mine gas concentration prediction method based on optimization variation modal decomposition according to claim 4, wherein when a KELM prediction model based on JAYA optimization is respectively built for each IMF, a kernel function is introduced, the kernel function matrix is Ω KELM＝HHT, the element is Ω KELM(i,j)＝h(xi)h(xj)＝K(xi,xj), and then the output of KELM is:
Wherein: i is a diagonal matrix, C is a regularization coefficient, and T is a desired output matrix;
KELM is a RBF kernel function, and the formula is:
Where λ is the kernel parameter.
6. The mine gas concentration prediction method based on optimized variation modal decomposition according to claim 5, wherein the nuclear parameter of KELM and the regularization coefficient are optimized by using JAYA, wherein the fitness evaluation function is:
wherein: y (i) is a prediction result, and y d (i) is a desired output.
7. The mine gas concentration prediction method based on optimal variation modal decomposition according to claim 4, wherein Step4 specifically comprises the steps of:
Step4-1, dividing the data according to windows, and predicting the data by JKELM to obtain n-m predicted gas concentration data;
Step4-2, performing difference between the predicted gas concentration data and the actual value to obtain layer 1 error data E 1, continuously predicting E 1 to obtain m-2n predicted error data, namely layer 2 error data E 2, and so on, and obtaining m-in predicted error data, namely layer i error data E i in the ith layer;
step4-3, setting the termination condition of error calculation as follows: 5|E i-Ei-1|0＜Ei-1.
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